"We must now review whether in future we should take a more critical stance” on selling arms to Saudi Arabia, Gabriel, who is also Germany's economy minister, said on Monday.
Berlin has in the past refrained from selling the Heckler & Koch G36 assault rifle and other offensive military weapons to Saudi Arabia.
On Friday, the Saudi regime executed prominent Shia cleric Sheikh Nimr al-Nimr, a senior opposition figure, and 46 others for what is called undermining national security of the kingdom.
The move was condemned as a violation of human rights across the globe.
Saudi Arabia severed diplomatic relations with Iran following demonstrations held in front of the Saudi embassy in Tehran and its consulate in the northeastern city of Mashhad by angry protesters censuring the Al Saud family for the killing of the top cleric. Some people mounted the walls of the consulate in Mashhad while incendiary devices were hurled at the embassy in Tehran. Some 50 people were detained over the transgression.
Meanwhile, German Chancellor Angela Merkel's spokesman Steffen Seibert called on both Saudi Arabia and Iran to make every effort to improve their diplomatic ties, emphasizing that Saudi-Iranian ties are "of fundamental importance for resolving the crises in Syria and Yemen and for the stability of the entire region."
Germany's opposition Greens and Left parties demanded that Berlin halt all military exports to Saudi Arabia, which reached 209 million euros ($226 million) in 2014, the last full year for which data is available.
Asked whether Germany planned to sanction Saudi Arabia, Seibert stressed that "it is in the interest of Germany to have dialogue with Saudi Arabia."
French Foreign Minister Laurent Fabius, meanwhile, has also called for a "de-escalation of tensions" between Riyadh and Tehran, government spokesman Stephane Le Foll said.
"France has an important role in this region as an interlocutor with all the parties," Le Foll said following a cabinet meeting.
The deteriorated diplomatic relations between Riyadh and Tehran "is hugely concerning because of course we want to see stability in the Middle East... not least because that will be absolutely essential for solving the crisis in Syria which is the source of so many of these problems," said British Prime Minister David Cameron.
"We condemn and do not support the death penalty in any circumstances and that includes Saudi Arabia," Press TV reported.
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